1) As far as I know, there is no limitation on what you HAVE to be in D&D, hence there being evil paladins, weak but dexterous fighters, Intelligent Sorcerers, and wise Wizards. An archetype does not by any means limit what you are allowed to do, and I would happily allow anyone to play a charming Barb, and am actually bored, just by the idea of another big stupid swinger of great axes.
In any RPG, the rules of the game reflect the reality of the game world, but they need to make a lot of assumptions in order to get the ruleset down to something that's actually
playable (and hopefully
fun). That's why the rules in the book cover a lot of situations that arise during gameplay, but aren't especially good for describing how NPCs operate behind the scenes. Many of the rules don't really make sense when you take them out of the context that they were designed to cover.
One of the big assumptions about D&D, as compared to a lot of other games, is that playable characters (the ones we care most about modeling) hew fairly closely to certain archetypes, which are the in-game reality that the classes
reflect. And the more detailed they build the classes, the more assumptions they need to make about the characters. Why do rogues learn thieves' cant, for example? It's because the game assumes "During your rogue training you learned thieves’ cant, a secret mix of dialect, jargon, and code that allows you to hide messages in seemingly normal conversation," and "In addition, you understand a set of secret signs and symbols used to convey short, simple messages, such as whether an area is dangerous or the territory of a thieves’ guild, whether loot is nearby, or whether the people in an area are easy marks or will provide a safe house for thieves on the run." That's a
pretty big assumption to make about your character, but it has to be true, or else they wouldn't be able to include it as a class feature; and that's just a minor aspect of the class.
And some classes make fewer assumptions than other classes. The fighter class, for example, assumes that you know how to use various weapons and armors (or can figure it out easily enough); it assumes that you have practiced one style of fighting more than others; and it assumes that you spend a lot of time making weapon attacks, which is
why you get so much better at them as you gain levels in the class. If you hardly ever used a weapon, then there's no reason why you would gain the Extra Attack feature, which
describes how much better you are with making weapon attacks. The class doesn't even assume whether you use a rapier, greatsword, or bow; which is why its features work equally well with all of them.
The barbarian class, along with the monk and (in earlier editions) the paladin, represent some of the
most narrow archetypes in the game. They have to make
more assumptions about your character, in order for the class progression to make sense, than they have to make about fighters or rogues or wizards. A barbarian gets mad, and then charges into combat with a big melee weapon. If that
wasn't true, then they wouldn't be justified in gaining their rage feature, which only grants a bonus to Strength-based weapons.
Of course, there's nothing saying that you
can't have a barbarian who is
also charming, but if you talked your way through most problems instead of charging at them with an axe, then you're violating the design assumption that forms the basis of the class in the first place. The progression of barbarian class features does not accurately
reflect the sort of social character you are describing.